^Now you are raising a different issue that you need to consider. When you put two choices, you are considered for first, and then if rejected, considered for second, and then if rejected, considered for Division of General Studies (at least if you are in-state). In other words, you three chances of being admitted.
If you put only one major, you will be considered for that, and if rejected, you are done. There will be no consideration for another choice or Division of General Studies.
In other words, if attending UIUC is important to you, you should provide two majors.